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Chapter 5 Analysis of Box Culvert, Results & Design

Chapter 5

Analysis of Box Culvert, Results & Design

5.1 Introduction

~\nalysis of Box Culvert was performed in SAP 2000. The box culvert should be

designed considering the following issues.

• It should be able to discharge the volume expected during a design flood.

• The structure of drainage culvert should be designed to be stable against the dead

, superimposed dead, live and earth pressure.

5.2 Load Cases

l'ollowing load cases are to be taken in to account( since culvert is used as underpass)

I. Vehicles at Top- No vehicles at Bottom

1.1 HA only

1.2 HA & HB only

2. No Vehicles at Top- No vehicles at Bottom

2.1 No HA or HB

3. No Vehicles at top- vehicles at bottom

3.1 HA only

3.2 HA & HB only

4. Vehicles at Top & Bottom both

4.1 HA only in top & bottom both

4.2 HA in top & bottom & HB in bottom only

4.3 HA & HB in top & bottom both

4.4 HA in top & bottom & HB in top only

31

~ ~;;(-'. v<~~ \ ;',

•


5.3 Loads on the Box Culvert

Traction Force

tit t t t t t tt ii tiJii+ Superimposed dead load

ttttt t tt ttttttttt. Live loads

tt t t t t t t tt tt iJ tttt Weight of soil

ttttt t tt titttttttt Weightofstrl}cture

Soil pressure

E 6 fttfttfttt tt t ttttt Reaction ofsoil

Figure 5.1 : Loads on the Box Culvert

~.3.1 Loads due to soil

Hydrostatic pressure

I kpending on the level of the stream, the box culvert can be either at the road level or

nuried. If it is buried, there will be soil on all four sides. Thus the following loads will act

.lue to the soil :

• The weight of the soil between the top slab and the road level acting on the top

slab.

• The soil pressure acting on the sides of the box culvert.

• If there is soil on the top slab, the soil loads will be transferred on to the side

walls.

5.3.2 Live Loads

l ive loads are generally due to vehicles traveling on the road. Live loads are calculated

according to BS5400.

32

~ . .0 ''"<,c •

. ~ .. :':

......


5.3.3. Loads on the top slab.

r op slab is loaded due to the weight of soil, super-imposed dead load of the road and live

loads due to vehicles.

5.3.4. Loads on the side walls

This consists of soil pressure and any surcharge pressure due to live loads.

5.3.5. Loads on the bottom slab

The soil below supports the box culvert. This soil is loaded due to the weight of the soil

above the box culvert, weight of the soil on the top slab, weight of the box culvert and

l1ve load on the box culvert. The average upward pressure is assumed on the bottom slab.

Jhis pressure is equal to all the loads divided by the bottom slab area.

5.3.6 Horizontal Live load due to traction

lhe structure shall be designed to resist the traction forces. Traction force shall be

applied perpendicular to the walls of the box culvert. Traction force was calculated as in

accordance with section 6.6 of BS5400 Part 2.

5.3.7. Hydrostatic Pressure

lhe effect of hydrostatic pressure must be taken in to account in the design of box

culverts. (either the selected structure is vehicular culvert). Because due to heavy rain if

water table increases to the high flood level in that area it will automatically generate

high hydrostatic pressure.

33

,,i) '"J<.'.

,,~~,.

' ' . ,,

..

;__"\lapter 5 Ana\ysis of Box Cu\vert, Results & Design

5.4 Modeling of Box Culvert

\nalysis of box culvert was performed using 20 shell elements of appropriate thickness.

'lnil was modeled as springs. Then the support conditions are taken as simply supported

tt its two ends.

)epending on the SPTN values of each soil type spring constants are calculated and

· abulated below.

Depth (measured from the culvert Spring Constants

top level) (in mm)

2675 8,000

2140 16,000

Below 2140 24,000

.;;,A.l Load Calculation

'.-tl.l Dead Load Calculation

>ead load may be calculated from SAP2000 finite element software automatically .

. .;;,A.l.2. Live load calculation

IIA. Loading

I DL shall be taken as 30kN per linear meter of notional lane.

IIA loading for the Top Slab

I !A loading for the Bottom Slab

30kN/m

30kN/m

34

~ . ,,~ ,,' ...• ~ ,'

...

hapter 5 Analysis of Box Culvert, Results & Design

HB Loading

·IB loading for the top slab

l fB loading for the bottom slab

30 units each 75kN

20 units each 50kN

<f. ~ <f. <f. axle axle illel4! axle

-·~ --

I I;

Ill -T+-- ~~ lm ·

t t·--- ---lll!it----'1~ --- r----Im I _

l . ----~--~ I T j I

-·~~---_1. • ''' - ··-- --·-· . -.

- 1.8 m 6 r---- --· + ----- -_m __ --+-- 1.~ m ..,

Figure 5.2: HB Vehicle Wheel Arrangement

;;,.t.l.3. Super Imposed Dead Load

\ ~sume 60mm surfacing

ompacted Density of Asphalt Concrete

oading from the surfacing

35

2450kg/m3

2450 X 0.06 X 5.35 X 9.81

7.72 kN/m

fJ.;;:. .:)"<,'.

·-~ .. ~ ' '


5.4.1.4. Reaction from Soil Calculation

Load Case 1.1 Total HA load in top slab = 30 X 10.8

= 324 kN

Super imposed load top slab = 7.72 X 10.8

= 83.38 kN

Super imposed load bottom slab = 7.72 X 10.8

= 83.38 kN

Volume of concrete = {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103.148m3

Weight of concrete = 103.148 X 24

= 2475.55 kN

Total downward load = 324 + 83.38 + 83.38 + 2475.55

= 2966.31 kN

Reaction from soil = 274.66 kN/m ~ "'"<('. '':l/~ ' ' Load Case 1.2 . ,,

Total HA load in top slab = 30 X 10.8

= 324 kN

Total HB load in top slab = 75 X 4 X 4

= 1200 kN

Super imposed load top slab = 7.72 X 10.8

= 83.38 kN

Super imposed load bottom slab = 7.72x10.8

= 83.38 kN

Volume of concrete = {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103.148m3

Weight of concrete = 103.148x24

= 2475.55 kN

Total downward load = 324 + 1200 + 83.38 + 83.38 + 2475.55

36

...

-

Chapter 5

Reaction from soil

Load Case 2.1 Super imposed load top slab

Super imposed load bottom slab

Volume of concrete

Weight of concrete

Total downward load

Reaction from soil

Load Case 3.1 Total HA load in bottom slab

Super imposed load top slab


Volume of concrete

Weight of concrete

Total downward load

Reaction from soil


= 4166.31 kN

= 385.77 kN/m

= 7.72x10.8 = 83.38 kN

= 7.72 X 10.8 = 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103. 148m3

= 103.148x24 = 2475.55 kN

= 83.38 + 83.38 + 2475.55 = 2642.31 kN

= 244.66 kN/m

= 30 X 10.8 = 324 kN

= 7.72x10.8 = 83.38 kN

= 7.72x10.8 = 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103. 148m3

= 103.148 X 24 = 2475.55 kN

= 324 + 83.38 + 83.38 + 2475.55 = 2966.31 kN

= 274.66 kN/m

37

' ' ''

....

,_'hapter 5

Load Case 3.2 Total HA load in bottom slab

Total HB load in bottom slab



Volume of concrete

Weight of concrete

Total downward load

Reaction from soil

Load Case 4.1 Total HA load in top & bottom slab



Volume of concrete

Weight of concrete

Total downward load

Reaction from soil


= 30 X 10.8

= 324 kN

= 50 X 4 X 4

= 1200 kN

= 7.72 X 10.8

= 83.38 kN

= 7.72 X 10.8

= 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 1 03.148m3

= 103.148x24 = 2475.55 kN

= 324 + 1200 + 83.38 + 83.38 + 2475.55 = 3766.31 kN

= 348.73 kN/m

= 30 X 10.8 X 2

= 648 kN

= 7.72 X 10.8

= 83.38 kN

= 7.72x10.8

= 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103.148m3

= 103.148x24 = 2475.55 kN

= 648 + 83.38 + 83.38 + 2475.55 = 3290.30 kN

= 304.66 kN/m

38

' .

-

Chapter 5





Volume of concrete

Weight of concrete

Total downward load

Reaction from soil


Total HB load in top slab




Volume of concrete


= 30x10.8x2

= 648 kN

= 50 X 4 X 4

= 1200 kN

= 7.72 X 10.8

= 83.38 kN

= 7.72 X 10.8 = 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103.148m3

= 103.148x24 = 2475.55 kN

= 648 + 1200 + 83.38 + 83.38 + 2475.55 = 4090.30 kN

= 378.73 kN/m

= 30x10.8x2

= 648 kN

= 75 X 4 X 4

= 1200 kN

= 50 X 4 X 4

= 800 kN

= 7.72 X 10.8

= 83.38 kN

= 7.72 X 10.8

= 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 1 03.148m 3

39

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'-

...

_·hapter 5

Weight of concrete

Total downward load

Reaction from soil


Total HB load in top slab



Volume of concrete

Weight of concrete

Total downward load

Reaction from soil


= 103.148x24 = 2475.55 kN

= 648 + 1200 + 800 + 83.38 + 83.38 + 2475.55 = 5290.33 kN

= 489.85 kN/m

= 30x10.8x2

= 648 kN

= 75 X 4 X 4

= 1200 kN

= 7.72x10_8

= 83.38 kN

= 7.72 X 10.8

= 83.38 kN

= {10.8 X ( 0.75 + 0.60) X 5.35} + 9 4.7 X 0.5 X 5.35 X 2)

= 103.148m3

= 103.148 X 24 = 2475.55 kN

= 648 + 1200 + 83.38 + 83.38 + 2475_55 = 4490.30 kN

= 415.77 kN/m

40

.~~ ·~,~~\

•'J:"s.\ ' ' . l:

-

Chapter 5

5.-t.l.S Lateral earth pressure calculation

Take Surcharge as 1 OkN/m2

Take Unclassified Soil

y = 18 kN/m3

<p = 30 dgrees

Consider at Rest condition

k0 = ( 1 - Sin <p )

= 0.5

Over-burden at top

Over-burden at 5350mm depth

Pressure Distribution

10.0 kN/m2

5.35m

58.15 kN/m2

41


= 10kN/m2

10+0.5x18x = 10 + kovH = 5.35

= 58.15 kN/m2

-


5.4.1.6. Traction force

BS5400 Part 2 Section 6.6 states that

For HA loading: Traction force= 8 x 10.8 +200 (but minimum 700kN)

Traction force from HA vehicle = 286.4 kN

For HB loading

Traction force for 30units of HB vehicle

Traction force for 20units of HB vehicle

= 75 X 25% X 8 = 150 kN

=50 X 25% X 8 = 100 kN

From the above calculations Traction force for HA vehicle> HB vehicle

Apply traction force of286.4kN from HA vehicle at the center of the notional lane.

5.-t.l. 7. Hydrostatic Pressure

Take the high flood level at the selected culvert area as 4.28m

Hydrostatic pressure = hpg = 4.28 x 1000 x I 0 I 1000 = 42.8 kN/m2

Equivalent UDL = 42.8 X 5.35 x0.5 X 42.8/42.8 = 114.49 kN/m

42


5.5 Concrete Outline Drawing of Box Culvert

RFL LINE

r- ~

I • . . • t ~I ·.~ . " . 4" " " . . j I. •. q,....._,. :...,...,. C"7"J . • 1

2

.35-o-mmTHK. CO-RBEL APPROACH SLAB

5Dmm THK : BUNOING CONCRETE ~ lii

~

4 ~ " ~ ~~'

L I - SCREED CONCRETE 15/stS __j 10800

Figure 5.3 :Concrete Outline of Box Culvert

5.6. SAP2000 model of the Box Culvert

'\ I .. " ->~- ~ '

I ~ -""

~ -~ - ~ \ I ~- -~ 4111 : 11 ... _j ... I .. ~ .., I ..

~ ~- l II >\- ' I >1 ~ ~ \ .. 'I I I .. i I

~ 11.- - 1 I 4- l l .i '\ J<i I Jl ~ .~< . <t I ~ I, \ ~ ~ ) ~ - . ~ ~ I • . I . ); I ... \ " -", .•. .l .. .. .~ ,J, \ Ji <I I 'I

Figure 5.4: Model of Box Culvert

43

~

....


5.7 Load Combinations

HA Only

Dead Weight = 1.15

Earth Pressure = 1.5

Superimposed Dead = 1.75

Live Load = 1.5

HAandHB

Dead Weight = 1.15

Earth Pressure = 1.5

Superimposed Dead = 1.75

Live Load = 1.3

5.8 Deformed Shape for Load Case 4.3

.,..

>-." ~ lo¥ .. ..... . M lt"'' 11'1. _ ..... . r ~r I

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Figure 5.5: Deformed shape of Mode I

44

I .I

j

Chapter 5 Analysis ofBox Culvert, Results & Design

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' jl ... '

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Figure 5.6: Deformed shape for Mode 2

5.9 Results from the SAP2000 Modeling

;<~·

1?-

.-------:1 12) Ill Ioiii (~

45

~

0\

~es

Lo

1.1

....

....

....

...

1 2

I···

··

2.1

3.1

,,,,,,,.

3.2

4.1

4.2

4.3

4.4

Mom

ent

kNm

/m

141.

50

241.

30

388.

65

17.5

3

124.

38

450.

50

164.

53

130.

44

332.

98 A

t 1

At2

A

t 3

At4

She

ar

Mom

ent

She

ar

Mom

ent

She

ar

Mom

ent

She

ar

Forc

e kN

/m

kNm

/m

Forc

e kN

/m

kNm

/m

Forc

e kN

fm

kNm

/m

Forc

e kN

/m

3.97

21

2.39

38

.56

159.

79

0.17

56

.74

108.

34

····

····

····

· I·

......

......

...

. ...

....

....

....

....

....

.

11.0

0 24

4.01

57

.96

86.9

1 0.

14

41.4

6 90

.28

0.80

17

9.50

47

.30

162.

70

0.27

12

4.75

11

7.56

...

......

. I

......

... I

......

......

...

......

......

··

····

····

····

···

......

...

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3.32

35

8.85

82

.67

133.

14

0.18

51

.15

184.

27

0.52

38

.50

25.2

1 31

.04

0.07

18

.79

9.51

1047

.50

488.

35

100.

68

133.

14

0.18

11

3.63

34

9.77

28.3

5 53

.45

2.99

14

.56

0.05

56

0.08

19

6.67

48 8

1 4.

75

2.66

9.

94

0.07

57

0.46

20

3.41

5.12

9.

69

1.49

86

.91

0.14

41

.46

90.2

8

Tab

le 5

.1

Re

sult

s fr

om t

he S

AP

2000

Mod

elin

g

;;;;;,-'-

/F"i/1

• •

'-_J

\.})

___ _

:;;)

#

At5

M

omen

t S

hear

kN

m/m

Fo

rce

kN/m

98.9

1 68

6 71

··

····

· ..

....

93.8

8 36

816

205.

24

9517

7 ··

··-·

,,,,,,,

....

....

...

14.5

5 95

1 22

302.

96

3627

9

413.

54

1050

75

373.

54

448.

49

956

56

310

46

93.8

8 45

1.02

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Pl ~

[Jl

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0 X

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